Development and implementation of novel numerical techniques for integrated optics and microwave planar structures

In this thesis, a novel numerical method for characterizing the electromagnetic modes supported by multilayer planar optical waveguides and a new formulation of the Method of Lines (MoL) for the static analysis of multi-conductor planar transmission line structures have been developed.;One purpose of this work is to develop an efficient and accurate numerical method to analyze planar lossless, lossy and active optical waveguides in anisotropic media. This method solves the dispersion equation in the complex plane via Cauchy's integration for a guided wave structure of interest. The method is applicable to lossless, lossy, active and ARROW waveguide structures and can handle both leaky and guided modes. Contrary to the methods currently published in the literature, which are based on a numerical derivative of the dispersion equation, we propose an analytical derivative for the latter. This has a double impact: improved accuracy and reduced CPU time. The specific integration contour for leaky modes is discussed. The results are in excellent agreement with several results published in the literature.;Another purpose of this work is to develop a new formulation useful for modeling the Quasi-TEM performance of multi-conductor transmission lines in inhomogeneous anisotropic media, including finite metallization thickness. A general Method of Lines (MoL) formulation for inhomogeneous anisotropic media and finite metallization thickness is derived. The method allows the accurate determination of the static parameters of the transmission line with great efficiency compared to methods available in the literature. Several numerical examples are shown for single and multi-conductor transmission lines including finite metallization thickness effect. Comparisons made with the results available from the literature validate the approach.